For more information, please visit: http://staff.ustc.edu.cn/~wangzuoq/Conferences/SGAGA2015/
Symplectic Geometry and Global Analysis Conference
The primary aim of the conference is to gather together experts in symplectic geometry and related areas
of global analysis to discuss recent advances and find possible new directions of research in these areas.
It also provide a good opportunity for young scholars and graduate students to enter this area.
Participants
Name
Institution
Email
陈柯
中国科学技术大学
kechen@ustc.edu.cn
冯仁杰
北京国际数学中心
renjie@umd.edu
李慧
苏州大学
hui.li@suda.edu.cn
李逸
上海交通大学
yilicms@sjtu.edu.cn
刘博
Humboldt University
boliumath@gmail.com
卢文
华中科技大学
wlu@hust.edu.cn
麻小南
法国巴黎七大
xiaonan.ma@imj-prg.fr
石亚龙
南京大学
shiyl@nju.edu.cn
宋百林
中国科学技术大学
bailinso@ustc.edu.cn
王宏玉
扬州大学
hywang@yzu.edu.cn
王作勤
中国科学技术大学
wangzuoq@ustc.edu.cn
许小卫
中国科学技术大学
xwxu09@ustc.edu.cn
杨晓奎
中国科学院数学与系统科学研究院
xkyang@amss.ac.cn
俞建青
中国科学技术大学
jianqing@ustc.edu.cn
周久儒
扬州大学
zhoujr1982@hotmail.com
朱家林
复旦大学上海数学中心
jialinzhu@fudan.edu.cn
Sponsers
?
School of Mathmatical Sciences, USTC
?
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, CAS
?
Tian-Yuan Foundation
Organizers
?
Xiaonan Ma （法国巴黎七大）
?
Zuoqin Wang （中国科学技术大学）
Contacts
?
Yuguo Qin sign42@mail.ustc.edu.cn
?
Weiwei Wang wawnwg123@163.com
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Time
From August 10 to August 11
Location
中国科学技术大学 管理楼 1518（靠近科大东区北门）
Accommodation
悦雅江南春酒店
合肥市金寨路 64 号（金寨路与太湖路交叉口）
Map
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Program
Date
Time
Speaker
Title
August 9
All Day
Registration
August 10 9:00-10:00
王宏玉 （扬州大学）
From Kodaira Conjecture to Donaldson question
10:00-10:30
Coffee break
10:30-11:30 李逸 （上海交通大学）
A geometric flow and Hopf's conjecture
11:30-14:00
Lunch break
14:00-15:00 李慧 （苏州大学）
The fundamental group of G-manifolds
15:00-16:00 刘博 (Humboldt University)
Geometric model for differential K-theory
16:00-16:30
Coffee break
16:30-17:30 卢文 （华中科技大学）
Optimal convergence speed of Bergman metrics on symplectic manifolds
18:00-20:00
Banquet
August 11 9:00-10:00
麻小南 （法国巴黎七大）
Toeplitz operator and vanishing theorem
10:00-10:30
Coffee break
10:30-11:30 朱家林 （复旦大学上海数学中心）
Gluing formula of analytic torsion and Scattering matrix
11:30-14:00
Lunch break
14:00-15:00 冯仁杰 （北京国际数学中心）
Extrema of random holomorphic fields
15:00-16:00 俞建青 （中国科学技术大学）
Higher Spectral Flow for Dirac Operators with Local Boundary Conditions
16:00-16:30
Coffee break
16:30-17:30 杨晓奎 （中国科学院数学与系统科学研究院）
The Kahler-Ricci flow and collapsing limits
Titles and Abstracts
Speaker: 王宏玉
(扬州大学
)
Title: From Kodaira Conjecture to Donaldson question
Abstract: In this talk, we show that any tamed closed almost complex four-manifold with self-
dual second Betti number one, there exists a new sympletcic form compatible with the given almost
complex structure, Then, we give an affirmative answer to Donaldson question for tamed closed
almost complex four-manifolds with self-dual second Betti number one. Our approach is along the
lines used by Buchdahl to give a unified proof of the Kodaira Conjecture.
Speaker: 李逸
(上海交通大学
)
Title: A geometric flow and Hopf’s conjecture
Abstract: In this talk, I will discuss a geometric flow recently introduced by Kefeng Liu and I on
vector fields. This flow has its nature both in geometry and PDEs, in particular, in connecting with
the long-standing two conjectures of Hopf and a problem of Yau.
Speaker: 李慧
(苏州大学
)
Title: The fundamental group of G-manifolds
Abstract: Assume a compact connected Lie group acting on a symplectic manifold. We will discuss
the fundamental group of the symplectic manifold, and that of the orbit space; when the Lie group
action is Hamiltonian, we also discuss the fundamental groups of all the symplectic quotients.
刘博
(Humboldt University)
Title: Geometric model for differential K-theory
Abstract: In this talk, by using family index theorem, eta form and higher spectral flow, we will
construct a new geometric model for differential K-theory on closed manifolds and define the push-
forward map. Furthermore, we will extend this model and the corresponding properties to the orbifold
case.
Speaker: 卢文
(华中科技大学
)
Title: Optimal convergence speed of Bergman metrics on symplectic manifolds
Abstract: It is known that a compact symplectic manifold endowed with a prequantum line bundle
can be embedded in the projective space generated by the eigensections of low energy of the Bochner
Laplacian acting on high p-tensor powers of the prequantum line bundle. We show that the Fubini-
Study metrics induced by these embeddings converges at speed rate 1/
p2 to the symplectic form.
This is a joint work with Professors Xiaonan Ma and George Marinescu.
Speaker: 麻小南
(法国巴黎七大
)
Title: Toeplitz operator and vanishing theorem
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Abstract: We will explain a criteria on the vanishing of the de Rham cohomology group associated
with a family of flat vector bundles, this is a real analogy of the vanishing theorem of Kodaira-Serre.
The theory on the Toeplitz operators plays an important role.
Speaker: 朱家林
(复旦大学上海数学中心
)
Title: Gluing formula of analytic torsion and Scattering matrix
Abstract: In this talk I will introduce our joint work with Martin Puchol, Yeping Zhang on the
gluing formula of analytic torsion. We give an analytic proof of the gluing formula of Brüning-Ma of
analytic torsion by using the adiabatic method and scattering matrix.
Speaker: 冯仁杰
(北京国际数学中心
)
Title: Extrema of random holomorphic fields
Abstract: In the first part of the talk, I will define the random holomorphic fields and exhibit several
well-known results. In the second part, two of my results on the extrema of random fields will be
given: the distribution of critical values and the mean value of the supremum of
L2-normalized fields.
I will also discuss several open problems.
Speaker: 俞建青
(中国科学技术大学
)
Title: Higher Spectral Flow for Dirac Operators with Local Boundary Conditions
Abstract: We consider a gauge invariant one parameter family of families of fiberwise twisted Dirac
type operators on a fiberation with the typical fiber an even dimensional compact manifold with
boundary, i.e., a family t
Duu
,u P [0
, 1] with
D1 =
gD0
g?1 for a suitable unitary automorphism
g of
the twisted bundle. Suppose all the operators
Du are imposed with a certain
local elliptic boundary
condition
F and
Du,F is the self-adjoint extension of
Du. We establish a formula for the higher
spectral flow of t
Du,F u,
u P [0
, 1]. Our result generalizes a recent result of Gorokhovsky and Lesch
to the families case. If time permits, I will also touch briefly on the equivariant higher spectral flow,
which is the potential joint work with Fei Han.
Speaker: 杨晓奎
(中国科学院数学与系统科学研究院
)
Title: The Kahler-Ricci flow and collapsing limits
Abstract: We discuss the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a
Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from
the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler
metrics. This strengthens previous work of Song-Tian and others. This is joint work with Ben
Weinkove and Valentino Tosatti.
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